Question 2
Let
$$f(x)=\frac1x+\frac1{x-2}+\frac1{x-4}+\cdots+\frac1{x-2018},\qquad g(x)=\frac1{x-1}+\frac1{x-3}+\frac1{x-5}+\cdots+\frac1{x-2017}.$$
Prove that $|f(x)-g(x)|\gt 2$ for every non-integer real number $x$ satisfying $0\lt x\lt 2018$.
$$f(x)=\frac1x+\frac1{x-2}+\frac1{x-4}+\cdots+\frac1{x-2018},\qquad g(x)=\frac1{x-1}+\frac1{x-3}+\frac1{x-5}+\cdots+\frac1{x-2017}.$$
Prove that $|f(x)-g(x)|\gt 2$ for every non-integer real number $x$ satisfying $0\lt x\lt 2018$.